Quantitative Aptitude

Quadratic Equations

367 Questions
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Quadratic Equations Questions

Multiple choice

In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer. I. x = 172 – 132 – 112 II. 4y2 – 13y + 9 = 0

  1. if x > y

  2. if x ≤ y

  3. if x ≥ y

  4. if x < y

  5. if x = y or relationship between x and y can't be established
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

x = 17^2 - 13^2 - 11^2 = 289 - 169 - 121 = -1. For 4y^2 - 13y + 9 = 0, roots are y = [13 +/- sqrt(169 - 144)] / 8 = [13 +/- 5] / 8. Roots are 18/8 = 2.25 and 8/8 = 1. Since x = -1 and both roots of y are positive, x < y.

Multiple choice

In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer. I. (x + 22) (x – 22) = – 123 II. y2 – 43y + 462 = 0

  1. if x > y

  2. if x ≤ y

  3. if x ≥ y

  4. if x < y

  5. if x = y or relationship between x and y can't be established
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

I: x^2 - 484 = -123 => x^2 = 361 => x = 19 or -19. II: y^2 - 43y + 462 = 0 => (y-21)(y-22) = 0 => y = 21 or 22. Comparing values, x < y in all cases.

Multiple choice

In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer. I. x2 + (343)1/3 = 56 II. (y)4/3 × (y)5/3 – 295 = 217

  1. if x > y

  2. if x ≤ y

  3. if x ≥ y

  4. if x < y

  5. if x = y or relationship between x and y can't be established
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Equation I: x^2 + 7 = 56 => x^2 = 49 => x = 7 or -7. Equation II: y^(4/3 + 5/3) - 295 = 217 => y^3 = 512 => y = 8. Comparing x and y, x is always less than y (7 < 8 and -7 < 8).

Multiple choice

Directions: Two equations I and II are given below in the following question. You have to solve these equations and give your answer. 2x2 – 7x + 6 = 0 y2 – 9y + 20 = 0

  1. if x < y

  2. if x > y

  3. if x ≤ y

  4. if x ≥ y

  5. if x = y or no relation can be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Solving 2x^2 - 7x + 6 = 0 gives (2x-3)(x-2) = 0, so x = 1.5 or 2. Solving y^2 - 9y + 20 = 0 gives (y-4)(y-5) = 0, so y = 4 or 5. Since all values of x are less than all values of y, x < y.

Multiple choice

Directions: Two equations I and II are given below in the following question. You have to solve these equations and give your answer. 2x2 – 21x + 55 = 0 2y2 – 17y + 36 = 0

  1. if x < y

  2. if x > y

  3. if x ≤ y

  4. if x ≥ y

  5. if x = y or no relation can be established
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Solving 2x^2 - 21x + 55 = 0: roots are 5.5 and 5. Solving 2y^2 - 17y + 36 = 0: roots are 4 and 4.5. Since all x values (5, 5.5) are greater than all y values (4, 4.5), x > y.

Multiple choice

Directions: Two equations are given in the question. You have to solve these equations and give answer accordingly. x2 – 17x + 72 = 0 y2 – 21y + 110 = 0

  1. x > y

  2. x < y

  3. x ≤ y

  4. x ≥ y

  5. x = y or no relation can be established.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

x^2 - 17x + 72 = 0 => (x-8)(x-9) = 0, so x = 8, 9. y^2 - 21y + 110 = 0 => (y-10)(y-11) = 0, so y = 10, 11. Comparing the sets, every value of x is less than every value of y, so x < y.

Multiple choice

Directions: In this question, two equations numbered I and II are given. You have to solve both the equations and choose the correct option accordingly. I. x2 - 10x + 24 = 0 II. y2 - 14y + 48 = 0

  1. x < y

  2. x ≤ y

  3. x > y

  4. x ≥ y

  5. x = y or the relationship cannot be established
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Solving I: x^2 - 10x + 24 = 0 gives (x-6)(x-4)=0, so x=6 or 4. Solving II: y^2 - 14y + 48 = 0 gives (y-8)(y-6)=0, so y=8 or 6. Comparing the sets {4, 6} and {6, 8}, we see x is always <= y.

Multiple choice

Directions: Solve the given equations and identify the correct answer. 10x2 - 20x - 80 = 0 y2 + 13y - 68 = 0

  1. x > y

  2. x ≥ y

  3. x < y

  4. x ≤ y

  5. x = y or relation cannot be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Solving 10x^2 - 20x - 80 = 0 gives x^2 - 2x - 8 = 0, so (x-4)(x+2)=0, x=4 or -2. Solving y^2 + 13y - 68 = 0 gives (y+17)(y-4)=0, y=-17 or 4. Comparing the sets, x >= y is true because the maximum value of x is 4 and the maximum value of y is 4, and all other combinations satisfy the inequality.

Multiple choice

I) 2x2 + 28x + 98 = 0 II) y2 + 20y + 91 = 0 In the following questions, two equations I and II are given. You have to solve both equations and give answer as, a) If x > y b) If x ≥ y c) If x < y d) If x ≤ y e) If x = y or the relation cannot be established.

  1. A

  2. B

  3. C

  4. D

  5. E
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Equation I factors as (x + 7)^2 = 0, so x = -7. Equation II has roots -7 and -13, so every possible value of y is less than or equal to x. Therefore, x >= y.

Multiple choice

Directions: The following question consists of two equations. You are required to solve the equations and identify the correct answer from the alternatives given below. I. 2x2 + 13x + 20 = 0 II. 2y2 - 11y + 12 = 0

  1. x ≥ y

  2. x ≤ y

  3. x > y

  4. x < y

  5. x = y or no relation can be determined
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

I. 2x^2 + 13x + 20 = 0 => (2x+5)(x+4) = 0 => x = -2.5, -4. II. 2y^2 - 11y + 12 = 0 => (2y-3)(y-4) = 0 => y = 1.5, 4. Comparing all values, x < y.